Syllabus of Higher Secondary
Standard 8-9-10
Implemented From June - 2004 in Standard - 8,
Implemented From June - 2005 in Standard - 9,
Implemented From June - 2006 in Standard - 10

Standard 9
Maths

Standard - 8 | Standard - 10

Number Sets

(1) Set theory

• Basic concept of Set - undefined elements.

• Symbols (notations) related to set: { },Î, Ï

• Methods of denoting set. ( l ) list method.

• (ii) the method of describing by use of properties.

• Types of set

  • null set { }, Æ

  • singleton set

  • subset Ì

  • universal set È

  • complement of a set

  • finite set and infinite set

  • equal sets

  • Equivalent set

• Set operations (1) Intersection of sets (ii) Union of sets. (iii) union

• Venn diagram for (1) two sets (ii) three sets (iii) set operations using Venn diagrams.

(2) Real numbers

• Rational and irrational numbers ( revision- rational numbers)

• Irrational numbers as infinite non- recurring decimals.

• Approximate values

• Sets of numbers

  • The set of natural numbers N (relations Venn diagrams)

  • The set of integers Z

  • The set of rational numbers Q

  • The set of real numbers R
    N Ì Z Ì Q Ì R

• The principle of Pythagoras -the representation of ~2 ~5 on the number line using it.

• (introduction of both methods and construction).

• Properties of addition and multiplication in R

  • closure property

  • commutative property

  • associative property

  • distributive property

• Identities (i) Additive identity (ii) Multiplicative identity

• Additive and multiplicative inverses.

• Subtraction and Division in R.

• Some important results ( if a, b , c are real nos. then)

  1. a x O=O

  2. if ab = 0 then a=O or b = 0

  3. (-a)(b)= - (ab) = a(-b)

  4. (-a)(-b)=ab

  5. a(b - c) = ab - ac

• Equalities and inequalities

• -Order, relation between numbers

• Equality

• Postulates of equality for real nos a , b , c.

• 1) Reflexivity a= a

• 2) Symmetry if a b then b a

• 3) Transitivity if a b, and b c then c = a

• 4) Ifa=bthena+c=b+candae.bc

• Inequalities

• Postulates of inequalities

• 1) lf a>0, b>0 then a+b>0

• 2) lf a>0, b>0 then ab>0

• 3) If a < 0 if and only if -a >0

• Some important results of inequalities

• 1) a - b > 0 if and only if a > b

• 2) if a>b and b>c then a>c

• 3) if a>b then a+c>b+c

• 4) if a>b and c>0 then ac>bc

• 5) if a > b and c < 0 then ac < bc

• 6) if a > b and c > d then a +c > b+d

• (important symbols like ¹, ³, <=, >, <, <, > exam- pies to be given)

• The representation of inequalities on the number line.

• The absolute value of magnitude of a number.

(3) Rational Indices

• Index

• Laws of indices
  1) Law of multiplication a^m x aⁿ, = a^m+n
  2) Law of Division : a¹0, if rn > n then a m ¸ a n=a^m-n
  If n> m then a^m ¸ aⁿ = 1/a^n-m
  And m=n then a^m ¸ aⁿ = 1

• 3) The law of power of a power
  (am)ⁿ = a^mn

• 4) Law for the power of multiplication.
  (ab)^m = a^m . b^m

• 5) Law for the power of division (a ¸ b) m = arn (b ¹ 0) b rn
  or (a/b)^m = a^m b^m (b ¹ 0)

• 6) Zero and negative integral indices
  - for every a ¹ 0 a⁰ = 1
  - if n is positive integer and a ¹ 0 then
  a^-n = a^1/n

• The nth roots of Real numbers.

• Fractional indices - ( laws as above) (Laws to be added) Arithmetic

(4) Profit - Loss (percentage)

• Revision

• Calculations of profit - loss when profit-loss rates are given.
  (numerical of profit-loss & percentage)
  (Examples should be more difficult compared to previous classes)

• To calculate profit - loss percent when profit - loss given.

• Numerical of discounts (in percentage) (on printed price)

• Profit percent after giving discount.

(5) Simple interest - Compound interest , Amount

• Formula to calculate simple interest, explanation of notations used in the formula.

• Method of calculating simple interest - numericals

• Formula to find compound interest (every year) and explanation of notations used.

• Difference between simple interest and compound interest and their calculations (numericals).
  (sums of finding N.P.R in simple interest and compound interest)
  [more than three years should not be taken ]
  (simple examples of finding N. P R in addition of yearly interest at compound interest examples of finding N. P R at simple interest) Algebra

(6) Identities and Factorization

• Revision of identities and factorization done in std. VII
  (card board model to be used for the explanation of identities)
  (related factorization should be taken corresponding to identities)

• (x+a)(x+b) = x² +(a+b)x + ab

• (x+ y)³ =x³ + y³ +3xy(x+y)

• ( x + y + z )² = x² + y² + z² + 2xy +2yz +2zx

• x² + bx + c

(7) Division of polynomials (one variable & maximum 4th index power)

• Introduction of polynomials on the basis of variable and index. (addition)

• (when a=1 sum of an²  + bn +c)

• To divide monomial by monomial

• To divide polynomial by a monomial

• To divide polynomial by binomial

• To divide polynomial by polynomial

• Dividend = divisor x quotient + remainder using this formula / explanation of concept of factorization / division

(8) Equations

• ax + b = k (cx + d ¹ 0) solution of equation scx + d

• Problem sums

(9) Geometry

(1) Structure of geometry

• Undefined terms, definitions , postulates and theorems

• Types of proof of theorem:- direct and indirect

• Special phrases

• At the most

• At least

• One and only one

• Only if

• If and only if

(2) Point , line and idea of distance

• Point

• Line

• Postulate 1 . A line contains atleast two distinct points.

• Postulate 2. Two distinct points lie on a unique line.,

• Collinear and non- collinear points.

• Intersection of two sets.

• Theorem If two distinct lines intersect each other in a point they do not do so in another point. (without proof)

• Betweenness

• Idea of distance

• Postulate 3 (distance postulate)
  A unique non- negative real number corresponds to each pair and points the correspondence is called the distance between the two points.

• Measuring distance - use of modulas (absolute value)

• Postulate 4 ( Ruler postulate )
  1) To every real number there corresponds a unique point on a line.
  2) To every point of a line, there corresponds a unique real number.

• 3) There exists 1-1 correspondence between points on a line and real numbers such that distance between two points is equal; to the absolute difference of numbers corresponding to these points.

• Postulate 4a
  Given two distance points A and B on a line there exists a 1 -1 correspondence of postulate 4 such that zero corresponds to A and a positive number corresponds to B.

(3) Line segment and Ray

• Line segment - definition with set notation

• Congruent line segments- mid point of line segment.

• Theorem -every line segment has unique midpoint (without proof)

• to find midpoint by formula method.

• Definition of ray and set notation

• Opposite rays

• Point plotting on a ray

• Bisector of a line segment.

(4) Plane

• Idea of a plane

• Postulates of a plane

• Postulate 5 - every plane contains atleast three non-collinear points.

• Postulate 6 - Three non-collinear points detrermine a unique plane,

• Coplanar and non -coplanar points

• Postulate 7 - a line through two distinct points on a plane is a subset of the plane.

• Coplanar and Skew lines

• Theorem - A unique plane passes through a line and a point outside it. (without proof)

• Theorem :- A unique plane passes through two distinct intersecting lines.

  • Intersection of two planes ( two parallel lines determine a unique plane

  • Postulate 8:-the intersection of two distinct intersecting plane is a line.

  • The angles subtended by two congruent minor arcs at the centre are congruent & its converse.

(5) Congruent chords are equidistant from the centre and its converse.

• The measure of the angle subtended by a minor arc of a circle at the centre is twice the measure of the angle subtended by that arc at any point on the remaining part of the circle.

•  (1/2, problems based on this property) construction of an angle.

(6) construction of angle using scale and compass. (multiple of 15⁰).

• To construct an angle congruent to a given angle.

• Construction of an angle bisector.

(10) Mensuration

• Area and volume

• Area

• Cone and sphere.

• Curved surface area of cone & sphere

• Curved surface area of cone.

• Curved surface area of sphere.

(11) Volume of cone and sphere

• Volume of cone

• Volume of sphere

• Simple examples based on curved surface area and volume

• Direct problem sums involving curved surface area and volume of one solid (simultaneously) can be given.

(12) Statistics

• Classification of data

• Score - one measure

• Data

• Qualitative and Quantitative data.

• Classification of Qualitative data.

• Classification of Quantitative data.

• Some definitions

• Lower, limit, upper limit, midvalue upper limit point lower limit point class length, mean (number of observations not exceeding 10)

Standard - 8 | Standard - 10

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